I find it ironic that the accident occurred, noise you have may be caused by 25 different reasons from that type of Collision.
Was the Frame bent, or was it unchecked for one reason or other? Was it Totalled? You checked the Tranny lines to the Radiatot, no obstructions inside?
The Valve Cover being struck, that damaged may indicate possible noise due to Valvetrain Damage, as seen; the Cam Timing Sprocket being positioned high above the Valve Cover & other components, a hard strike may bend the Gear & thrust the entire Cam backward and misalign Tensioners below the Lobes, and bend or break the Tensioners(s) themselves. Pic:
The Timing Chains are VERY long to begin with, doesn’t take much to upset the balance.
Did you check the Starter, examine the Flexplate housing that Bolts up looking for any interference with the lower back on Shroud(s) removed, or by a Buddy rotating the Motor by the Crank Pulley with a Socket & Ratchet by hand, (Coil, Battery disconnected)
On JACKSTANDS, not just a Jack.lift Car, did you try the suggestions I’d left you in the 1st email? What were the results? Universals,?Gears, Pinion Bearing & angle OK?
A few other Diagnostics and quick solutions, that’ll point you in the right direction. Torque Converter Test....Transmissions can shudder in a very similar manner to torque converters. To determine whether the shudder is tranny or TC related, run your vehicle for a little while till it begins to shudder and immediately park it. With your foot on the brake, put the transmission in Drive, and apply light throttle. If you feel shuddering, then it's likely the Torque converter. Most Transmission problems are not serious,!but will become serious if not repaired quickly.
Unless there is physical damage to the converter or transmission from the accident, “shudder” is a fairly easy problem to solve. Once the transmission fluid has been overheated enough times, it becomes permanently de-polymerized and need to be Cleaned, in some rare cases- replaced. It’s not difficult & You can do this yourself by draining the transmission and flushing it, several times. or taking it to any competent Shop for Transmission Maintenance.
The alternative repair is a Transmission Fluid Viscosity enhancer. Lucas brand is the most popular and works well, but usually the most expensive, contains friction modifiers that the stock Dextron does not, don’t use F type in your 02’ GT!nZuse the Additive & Non Synthetic Oil. Engine is hot and running when Oil level is checked? (Sorry, has to ask- some do not do this).
I’d also replace the Rear end Lube, Whale Oil worked the best- good luck finding that, use a high quality OEM Oil.Good luck! John